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| Book/Report | FZJ-2018-07045 |
;
1994
Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag
Jülich
Please use a persistent id in citations: http://hdl.handle.net/2128/20287
Report No.: Juel-2973
Abstract: The following paper is devoted to the study of Bohm's criterion for a magnetized plasma in contact with a neutralizing wall, when the magnetic field is inclined (oblique) with respect to the wall. A typical phenomenon, which has been studied both numerically [1] and recently also in analytical form [2] by considering polarization (inertial) drift terms, is the formation of a quasineutral magnetic presheath in front of the genuine (space charge) Langmuir sheath adjacent to the wall. The magnetic presheath is preceded (towards the plasma) by a source and (depending on the collisionality) friction determined presheath [3]. Due to the complexity of the problem the sheath formation and the correlated Bohm criterion at the entrance of the magnetic presheath (from the plasma side) have only been investigated for a strictly ID case, in which the electric field has only a component perpendicular to the wall. If also the magnetic field is directed perpendicular to the wall, the magnetic presheath disappears and the purely electrostatic case is recovered, which recently was generalized to cover plasmas with several ion components [4]. However, for application in magnetic fusion devices, where the plasma edge is in contact with limiters or divertor targets, an electric field component tangential to the wall must also be considered. This electric field component disappearing at the wall surface (assumed to be ideally conducting) is related to an antiparallel electron temperature gradient in the plasma. It produces an electric drift, which transports particles and energy to the wall (in contrast to the divergence-free magnetization part of the $\overrightarrow{\bigtriangledown}$p$_{\perp}$ drift [5]) and renders the problem, strictly speaking, 2-dimensional with wall-tangential gradients of the ion distribution function appearing in Bohm's criterion. It will be shown that under certain assumptions concerning the decrease of the tangential electric field component when approaching the wall and concerning the gradient length (tangential to the wall) of the ion distribution function at the entrance of the magnetic presheath, Bohm's criterion may be treated in a quasi 1D form. Adopting as already proposed in ref.[10] a step-like form for the ion distribution function, we recover in case of cold ions (with respect to their gyro-motion) - apart from the absence of a diamagnetic drift contribution - the form already used as boundary condition in 2D fluid calculations for tokamak plasmas in contact with toroidal limiters [6]. In order to obtain also meaningful results for thermal ions, we presuppose an ion gyro-cooling (or scrape-off) effect at the entrance of the magnetic presheath. This effect will be treated in a forthcoming paper. The present paper is organized as follows : In the first part we give a survey of the already existing theory in the strictly 1D case including the equations for the particle orbits, the constants of motion, from which - in principle at least - the loss cones in velocity space may be derived, the drift velocities including inertial (polarization) effects, the resulting Bohm criterionand its generalization for a multi-ion plasma. In the second part we extend the theory to incorporate an electric field component tangential to the wall. The conditions will be defined, under which a quasi-1D treatment of the problem is possible leading to a characteristic modification of Bohm's criterion at the entrance of the magnetic presheath, both for a single-ion (simple) and a multi-ion plasma.
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